Here is a little trick to find out if one in your friendlist is Offline or Invisible :
If you are Gmail user:
1. Open the chat window by clicking your friend’s name
2. Click on Options and select Go off the Record
3. Send some message to the user.
4. If you get the feedback from gtalk that User is offline and can’t receive messages means that the user is really offline.
5. But if you get no response that means that the user is appearing offline and in invisible mode.
If you are Gtalk User:
All the steps are same except 2. Here Click on the Down Arrow below the name in the chat window and select Go off the Record